Jannis from Long Bay showed he understood
the effect of combining transformations. Well done Jannis.
R2=I (reflecting twice is the identity).
So R3=R, R4=I.
I noticed that if there is an even number of Rs the result is the same as I.
If
there is an odd number of Rs the result is the same as R.
R2006=I as 2006 is even.
S is clockwise rotation by 90° about the origin.
So S2 is clockwise rotation by 180° about the origin.
S3 is rotation by 270° clockwise about the origin
(the same as S-1).
S4 is rotation by 360° about the origin (the same as I).
So S2006=S2 as S2000=I.
T is translation one unit to the right;
T2 is translation two units to the right;
T3 is translation three units to the right, and so on.
T2006 is translation 2006 units
to the right.
R S is not the same as S R.
R T2 is not the same as T2 R.
(R T)S is not the same as S(R T).
However, changing the order does sometimes produce the same transformation:
R S2=S2 R, for example.
The inverse of R S is (R S)-1=S-1R-1.
(S T)-1=T-1S-1.
(T R)-1=R-1T-1.
(R S2)-1=S-2R-1.